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  • A sealed container with a length of 0.3 m is filled with an ideal gas at a temperature of 500 K. The gas consists of 4.0 * 1023 gas molecules. Each molecule has a mass of 3.0 *&nbsp

A sealed container with a length of 0.3 m is filled with an ideal gas at a temperature of 500 K. The gas consists of 4.0 * 1023 gas molecules. Each molecule has a mass of 3.0 * 10−26 kg. Calculate the average force exerted by the gas molecules on the walls of the container, considering perfectly elastic collisions.

Option: 1

2.14 * 106 N


Option: 2

8.19 * 103 N


Option: 3

5.12 * 104 N


Option: 4

7.49 * 102 N


Answers (1)

best_answer

Given data:

Length of the container (L) = 0.3 m
Temperature (T) = 500 K
Number of molecules (N) = 4.0 * 1023
Mass of each molecule (m) = 3.0 * 10−26 kg
Boltzmann constant (k) = 1.38 * 10−23 J/K

Step 1: Calculate the root mean square (rms) speed of the gas molecules. The rms speed is given by the formula:

                    v_{rms} = \sqrt{\frac{3kT}{m}}

Substitute the given values and solve for vrms:

                 v_{rms} = \sqrt{\frac{3*1.38*10^{-23} * 500}{3.0 * 10^{-26}}} \approx 843.65 m/s

Step 2: Calculate the average force exerted by the gas molecules on the walls of the container. The average force can be calculated using the formula:

                    F = \frac{2mNv^{2}_{rms}}{L}

Substitute the given values and the calculated vrms and solve for F:

F = \frac{2*4.0*10^{23}*3.0*10^{-26}*(843.65)^{2}}{0.3}

        \approx 5.12 * 10^{4} N

 

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chirag

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